ISSN:0309-1929    

DOI:10.1080/03091928808208875

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

This is an attempt to predict the next fifteen years of geodynamo theory, and to assess the success potential of current directions of research. A new phenomenon, the subcriticality of a model-Z geodynamo, is described.

ISSN:0309-1929    

DOI:10.1080/03091928808208876

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

Finite amplitude solutions for convection in a rotating spherical fluid shell with a radius ratio of η=0.4 are obtained numerically by the Galerkin method. The case of the azimuthal wavenumberm=2 is emphasized, but solutions withm=4 are also considered. The pronounced distinction between different modes at low Prandtl numbers found in a preceding linear analysis (Zhang and Busse, 1987) is also found with respect to nonlinear properties. Only the positive-ω-mode exhibits subcritical finite amplitude convection. The stability of the stationary drifting solutions with respect to hydrodynamic disturbances is analyzed and regions of stability are presented. A major part of the paper is concerned with the growth of magnetic disturbances. The critical magnetic Prandtl number for the onset of dynamo action has been determined as function of the Rayleigh and Taylor numbers for the Prandtl numbersP=0.1 andP=1.0. Stationary and oscillatory dynamos with both, dipolar and quadrupolar, symmetries are close competitors in the parameter space of the problem.

ISSN:0309-1929    

DOI:10.1080/03091928808208877

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

The first three papers in this series (Fearn, 1983b, 1984, 1985) have investigated the stability of a strong toroidal magnetic field Bo=Bo(s*)Φ [where (s*. Φ, z*) are cylindrical polars] in a rapidly rotating system. The application is to the cores of the Earth and the planets but a simpler cylindrical geometry was chosen to permit a detailed study of the instabilities present. A further simplification was the use of electrically perfectly conducting boundary conditions. Here, we replace these with the boundary conditions appropriate to an insulating container. As expected, we find the same instabilities as for a perfectly conducting container, with quantitative changes in the critical parameters but no qualitative differences except for some interesting mixing between the ideal (“field gradient”) and resistive modes for azimuthal wavenumberm=1. In addition to these modes, we have also found the “exceptional” slow mode of Roberts and Loper (1979) and we investigate the conditions required for its instability for a variety of fields Bo(s*) Roberts and Loper's analysis was restricted to the case Bo∝s* and they found instability only form=1 and −1 <ω<0 [where ω is the frequency non-dimensionalised on the slow timescale τx, see (1.5)]. For other fields we found the necessary conditions to be less “exceptional”. One surprising feature of this instability is the importance of inertia for its existence. We show that viscosity is an alternative destabilising agent. The standard (magnetostrophic) approximation of neglecting inertial (and viscous) terms in the equation of motion has the effect of filtering out this instability. The field strength required for this “exceptional” mode to become unstable is found to be very much larger than that thought to be present in the Earth's core, so we conclude that this mode is unlikely to play an important role in the dynamics of the core.

ISSN:0309-1929    

DOI:10.1080/03091928808208878

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

The linear hydromagnetic stability of a non-constantly stratified horizontal fluid layer permeated by an azimuthal non-homogeneous magnetic field is investigated for various widths of the stably stratified part of the layer in the geophysical limitq→0 (qis the ratio of thermal and magnetic diffusivities). The choice of the strength of the magnetic field Bois as in Soward (1979) (see also Soward and Skinner, 1988) and the equations for the disturbances are treated as in Fearn and Proctor (1983). It was found that convection is developed in the whole layer regardless of the width of its stably stratified part. The thermal instability penetrates essentially from the unstably stratified part of the layer into the stably stratified part for A ∼ 1 (A characterises the ratio of the Lorentz and Coriolis forces). When the magnetic field is strong (A>1) the thermal convection is suppressed in the stably stratified part of the layer. However, in this case, it is replaced by the magnetically driven instability; which is fully developed in the whole layer. The thermal instabilities always propagate westward and exist for all the modesm. The magnetically driven instabilities propagate either westward or eastward according to the width of the stably and unstably stratified parts and exist only for the modem=1.

ISSN:0309-1929    

DOI:10.1080/03091928808208879

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

A system is considered in which electrically conducting fluid is contained between two rigid horizontal planes and bounded laterally by a circular cylinder. The fluid is permeated by a strong azimuthal magnetic field. The strength of the field increases linearly with distance from the vertical axis of the cylinder, about which the entire system rotates rapidly. An unstable temperature gradient is maintained by heating the fluid from below and cooling from above. When viscosity and inertia are neglected, an arbitrary geostrophic velocity, which is aligned with the applied azimuthal magnetic field and independent of the axial coordinate, can be superimposed on the basic axisymmetric state. In this inviscid limit, the geostrophic velocity which occurs at the onset of convection is such that the net torque on geostrophic cylinders vanishes (Taylor's condition). The mathematical problem which describes the ensuing marginal convection is nonlinear, and was discussed previously for the planar case by Soward (1986). Here new features are isolated which result from the cylindrical geometry. New asymptotic solutions are derived valid when Taylor's condition is relaxed to include viscous effects.

ISSN:0309-1929    

DOI:10.1080/03091928808208880

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

Plane layer αω-dynamo models are investigated. Travelling wave solutions are found: two critical dynamo numbers are shown to exist. At the first,Dc, dynamo action becomes possible. AsDis increased aboveDc, a regime is entered where core-mantle coupling is an essential part of the problem. At a second critical dynamo number,DT, Taylor's constraint is satisfied. AsDis raised beyond this value, nonlinear inviscid ageostrophic solutions satisfying Taylor's constraint have been computed.

ISSN:0309-1929    

DOI:10.1080/03091928808208881

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

This paper is concerned with a three-dimensional spherical model of a stationary dynamo that consists of a convective layer with a simple poloidal flow of the S2c2kind between a rotating inner body core and solid outer shell. The rotation of the inner core and the outer shell means that there are regions of concentrated shear or differential rotation at the convective layer boundaries. The induction equation for the inside of the convective layer was solved numerically by the Bullard-Gellman method, the eigenvalue of the problem being the magnetic Reynolds number of the poloidal flow (RM2) and it was assumed that the magnetic Reynolds number of the core (RM1) and of the shell (RM3) were prescribed parameters. HenceRM2was studied as a function ofRM1andRM3, along with the orientation of the rotation axis, the radial dependence of the poloidal velocity and the relative thickness of the layers for the three different situations, (i) the core alone rotating, (ii) the shell alone rotating and (iii) the core and the shell rotating together. In all three cases it was found that, at definite orientations of the rotation axis, there is a good convergence of both the eigenvalues and the eigenfunctions of the problem as the number of spherical harmonics used to represent the problem increases. ForRM1=RM3= 103, corresponding to the westward drift velocity and the parameters of the Earth's core, the critical values ofRM2are found to be three orders of magnitude lower thanRM1,RM3so that the poloidal flow velocity sufficient for maintaining the dynamo process is 10-20 m/yr. With only the core or the shell rotating, the velocity field generally differs little from the axially symmetric case. However, forRM2(orRM3) lying in the range 102to 105, the self-excitation condition is found to be of the formRM2˙R½M1=constant (orRM2˙R½M3=constant) and the solution does not possess the properties of the Braginsky near-axisymmetric dynamo. We should expect this, in particular, in the Braginsky limitRM2˙R−½;M1=constant.

ISSN:0309-1929    

DOI:10.1080/03091928808208882

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

An attempt has been made to include the axially asymmetric velocities into the calculation of Braginsky's Z-model of the nearly symmetric hydromagnetic dynamo. In this axisymmetric non-linear model dominated by Lorentz and Coriolis forces and maintained by a specified convection, the α-effect is prescribed. An example is shown of the axially asymmetric Archimedean buoyancy, which can imply an arbitrary alpha effect in the model with viscous core-mantle coupling. The formalisms of Tough and Roberts (1968) is also discussed and a modified α-effect in the Z-model is suggested.

ISSN:0309-1929    

DOI:10.1080/03091928808208883

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

The purpose of this note is two-fold: to draw attention to a perplexing difficulty connected with topographic core-mantle coupling, and to suggest tentatively an explanation. The difficulty is an apparent conflict between the most comprehensive theory of the coupling so far attempted (Anufriev and Braginsky, 1975a, b, 1977a, b) and recent explicit calculations based on magnetic and seismic information (Speithet al., 1986). It is argued that asymmetric deviations from Anufriev and Braginsky's basically axisymmetric model of the underlying core flow are capable of resolving the difficulty.

ISSN:0309-1929    

DOI:10.1080/03091928808208884

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor